Regensburg 2002 – wissenschaftliches Programm

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M: Metallphysik

M 8: Quasikristalle I

M 8.1: Fachvortrag

Dienstag, 12. März 2002, 09:30–09:45, H6

1D structures in a 2D quasicrystal: A new understanding of low quasicrystal conductivity? — •Eeuwe Sieds Zijlstra — Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, 70569 Stuttgart

The octagonal tiling is a two-dimensional quasiperiodic structure with eight-fold rotational symmetry. In this paper, I study conductivity and electron localization for a tight-binding Hamiltonian on the octagonal tiling. The relative strength of the potential and kinetic terms in the Hamiltonian forms a key parameter in this work. By means of a one-step renormalization procedure I calculate an effective Hamiltonian for the low kinetic energy limit. I show that in this limit the tiling splits up in clusters and chains. Only the chains contribute to the conductivity. The latter shows little variation with increasing size of the approximants. I then present strong numerical evidence that this result is not restricted to the low kinetic energy limit: when the kinetic and potential terms in the Hamiltonian are of comparable magnitude, the conductivity is still dominated by the chains for some values of the Fermi energy. The generality of these findings and the relevance for real quasicrystals are discussed.